Prove2Me

`BookProof.BookBrstYangMills.gaussGen_bracket` (c e : Fin N) : gaussGen G c * gaussGen G e - gaussGen G e * gaussGen G c = ∑ h, (G.f c e h) • gaussGen G h

Proved
BookProof.BookBrstYangMills.gaussGen_bracket

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.gaussGen_bracket (c e : Fin N) : gaussGen G c * gaussGen G e - gaussGen G e * gaussGen G c = ∑ h, (G.f c e h) • gaussGen G h

Formalization note: Lean 4 identifier BookProof.BookBrstYangMills.gaussGen_bracket.

Preamble
-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.gaussGen_bracket
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Mathlib
import Definitions.Def_ChapterBookBrstYangMills
import Definitions.Def_ChapterYangMillsGhostSector
open BookProof.YangMillsGhost
open BookProof.BookBrstYangMills



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge

noncomputable section

variable {N : ℕ} (G : GaugeAlgebra N)
Formal statement
theorem BookProof.BookBrstYangMills.gaussGen_bracket (c e : Fin N) :
    gaussGen G c * gaussGen G e - gaussGen G e * gaussGen G c
      = ∑ h, (G.f c e h) • gaussGen G h := by sorry

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